Transformations and Angle Relationships

Lesson 7

Math

Unit 3

8th Grade

Lesson 7 of 22

Objective


Describe sequences of transformations between figures using rotations and other transformations.

Common Core Standards


Core Standards

  • 8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.
  • 8.G.A.1.B — Angles are taken to angles of the same measure.
  • 8.G.A.1.C — Parallel lines are taken to parallel lines.
  • 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Foundational Standards

  • 4.MD.C.6

Criteria for Success


  1. Perform a combination of transformations, using rotations and other transformations, on a figure. 
  2. Describe a sequence of transformations with precision, using rotations and other transformations, between two figures (MP.6). 
  3. Understand that properties of transformations hold true even when there are multiple rigid transformations; for example, the side length of a polygon that is rotated and reflected is the same on the original figure and the transformed figure.

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Anchor Problems


Problem 1

Figure 1 is shown in the coordinate plane below. 

Which figure(s) would Figure 1 map to if it were

a.   Translated?

b.   Reflected?

c.   Rotated?

Guiding Questions

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Problem 2

Below is a picture of two rectangles with the same length and width:

a.   Show that the rectangles are congruent by finding a translation followed by a rotation that maps one of the rectangles to the other.

b.   Explain why the congruence of the two rectangles cannot be shown by translating Rectangle 1 to Rectangle 2.

Guiding Questions

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References

Illustrative Mathematics Congruent Rectangles

Congruent Rectangles, accessed on Oct. 13, 2017, 4:01 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Figures $${J, K, L, M, N,}$$ and $$P$$ are shown on the coordinate plane.

a.   Which figure can be transformed into Figure $$P$$ by a translation 2 units to the right followed by a reflection across the $$x$$-axis?

A. Figure $$J$$

B. Figure $$K$$ C. Figure $$L$$ D. Figure $$M$$

b.   Which figure can be transformed into Figure $$L$$ by a 90-degree rotation clockwise about the origin followed by a translation 2 units down? 

A. Figure $$J$$

B. Figure $$M$$ C. Figure $$N$$ D. Figure $$P$$

Guiding Questions

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References

PARCC Released Items Math Spring Operational 2015 Grade 8 End of Year Released ItemsProblem #10

Math Spring Operational 2015 Grade 8 End of Year Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Oct. 13, 2017, 4:02 p.m..

Problem Set

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Target Task


Problem 1

Triangle $${{ABC}}$$ is rotated $${90^{\circ}}$$ clockwise around the origin.

Which of the statements below are true? Select all that apply.

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Problem 2

Describe how you can use transformations to show that the two figures below are congruent.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Examples where students perform transformations that involve a combination of rotations and either reflections or translations to determine if two figures are congruent
  • Examples where students identify coordinate points of rotated vertices; be sure to include examples of rotations around the origin and around a point on a figure
  • Examples where students demonstrate understanding of properties of transformations
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Lesson 6

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Lesson 8

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Congruence and Rigid Transformations

Topic B: Similarity and Dilations

Topic C: Angle Relationships

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